Complex wavefunctions and electromagnetic waves

bhobba
Mentor
No one understands QM at a "intuitive" level.
Indeed.

You simply get used to it.

Thanks
Bill

No one understands QM at a "intuitive" level.
How then do you know you are getting the maths right if you can't see what it represents?

All of my thought processes depend on some sort of visual feedback to let me know that I am going in the right direction. Without it I get lost.

Personally, I'm happy with a a "shut up and calculate approach". This means just going along with the wave interpretation, and assuming the wave function evolves deterministically.

Like what happens to still liquid in a cup when the cup is jostled by a very little bit. The waves "localize" near the center. Same for QM. The wave does it's thing in response to its environment, and any attempts to measure cause it to ripple. In fact, we can estimate how our instrumentation modifies the wave function.

of course quantization and interacting particles make things more complicated.

bhobba
Mentor
How then do you know you are getting the maths right if you can't see what it represents? All of my thought processes depend on some sort of visual feedback to let me know that I am going in the right direction. Without it I get lost.
Like I say you get used to it.

Thanks
Bill

kith
A photon cannot be "localized" in a strict sense. One cannot even define a position operator in the strict sense for massless particles with spin $\geq 1$.
What do you think about Hawton's position operator? (see e.g. http://arxiv.org/abs/quant-ph/0101011) At the end of his FAQ entry, Neumeier criticizes that this operator isn't compatible with Lorentz invariance although Hawton has published a paper claiming the contrary in Phys. Rev. A (http://arxiv.org/abs/0804.3773).

kith
Kith, can you quote a source for this particular equation?
The quantity E+iB is called the Riemann-Silberstein vector. For a short overview of its use in both QM as well as classical physics, see http://arxiv.org/abs/1211.2655. You also find a couple of articles mentioning it if you search the arxiv for "photon wave function".

kith
No one understands QM at a "intuitive" level.
You simply get used to it.
Even though this is certainly correct in some sense, my impression is that such statements are often used to dismiss questions about the basics of QM which could improve one's understanding greatly. One example is the question about the complex nature of the wavefunction. The links to continuous transformations and generalized probability theories which allow for entanglement, for example, are quite recent achievements. Although the complex nature of the wavefunction can be traced back to these plausible fundamental principles, I often hear answers like "that's just how QM works", "no one really understands QM", "you just have to get used to QM's rules", etc. to this question. If people like Lucien Hardy hadn't followed their dissatisfaction with such answers, we would know a lot less about the foundations of QM.

So my advice is to try as much as possible to talk about things which don't "feel right" to you and to revisit your open questions from time to time. This is an ongoing process and every time I can relate something I have simply gotten used to to something fundamental, my understanding of QM enhances significantly.

That said, I think understanding QM above all means understanding its mathematics. Pondering too long on popularizations is counterproductive.

Many people only care about the rules. In order to solve a physical problem you always have to find an appropriate model. Although physics strifes for unification, you don't use the most fundamental model but the most simple one. Physicists are used to using different models for different situations without a practical need to relate these models.

The problem of the localization of the photon is a difficult problem which isn't relevant to many applications. Most people who know a good deal about QM (including me) simply haven't understood the details of it. For some people (again including me), understanding this problem better is still on the agenda while others don't consider it important for their understanding of QM and still others aren't even aware of it.

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bhobba
Mentor
If people like Lucien Hardy hadn't followed their dissatisfaction with such answers, we would know a lot less about the foundations of QM.
That's true.

In fact my personal opinion on the foundations of QM is Lucien Hardy's.

That said, having discussed such things, that approach leaves many cold. It's mathematically abstract being based on things like reversible continuous transformations that, for those into math, look pretty obvious, but if you aren't into that sort of thing can sort of leave you saying - so.

As I said I know this from discussing it with others and its exactly what they say.

Thanks
Bill

jtbell
Mentor
How then do you know you are getting the maths right if you can't see what it represents?
By working out solutions for situations that people have studied before, and comparing them to experimental results, or to already generally-accepted solutions. Gradually you develop a feel for it, and you gain confidence in applying it to new situations. As Bill said, "you get used to it."

Otherwise, how else can you understand this stuff? What is your secret?
To compliment f95toli's reply, there is a pair of books which make an attempt, and a pretty decent one, to make the mathematics of QM more plain and concrete. They also give a relatively accessible approach to understanding the derivation and application of QM math:

Visual Quantum Mechanics by Bernd Thaller
Advanced Visual Quantum Mechanics by Bernd Thaller